Please calculate the annualized $(252$ trading days$/$year$)$ historical volatility using the daily prices of

NYSE Euronext, Inc. $($NYX$).$

$4/1622\mathrm{.}13$

$4/1721\mathrm{.}87$

$4/2021\mathrm{.}38$

$4/2119\mathrm{.}62$

$4/2220\mathrm{.}55$

$4/2321\mathrm{.}45$

$($b$)($Continued with $($a$))$ The information about NYX and European call option is as follows: S$=22\mathrm{.}81,$

X$=20,$ rc$=2\mathrm{.}50\%($continuously compounded interest rate$),$ T$=21$ days. Calculate the Black$-$Scholes model

price for the European call option using the annualized historical volatility.

$($c$)$ Robert buys one call option contract on $100$ shares of NYX with the strike price of $$22\mathrm{.}5($the call

price$=$$$1\mathrm{.}81$ in the option market$)$ and sell one call option contract with the strike price of $$25($the call

price$=$$$0\mathrm{.}78).$ Both options contracts have the same maturity date. At option expiration, if the stock price

of NYX is $$24,$ what is the net profit$/$loss for all positions?

$($d$)($Continued with $($c$))$ Find the breakeven stock price for Robert$$s strategy.